1295. How many fractions must be added?

    Dear Teacher:

    If  there were  n  fractions and we rationalized all of them then

− √1 + √2 − √2 + √3 − √3 + √4 − √4 + √5 − √5 + √6 ...  =  − 1 + √(n+1)  =  1000

√(n+1)  =  1000 + 1  =  1001

n + 1  =  1001²  =  1002001

n  =  1002001 − 1  =  1002000  =  One million two thousand fractions.